To solve for  we must get all of the numbers on the other side of the equation of .

When solving a simple two-step equation we must remove the numbers that are interacting with  in this order: Addition/Subtraction, Multiplication/Division, Exponents.

To do this in a problem where  is being multiplied by a number, we must divide both sides of the equation by the number.

In this case the number is $\displaystyle 5$ so we divide each side of the equation by $\displaystyle 5$ to make it look like this $\displaystyle \frac{5x^{2}}{5}= \frac{245}{5}$

Our new problem will look like this $\displaystyle x^{2}=49$.

We then must solve the exponential equation.

To solve an equation with  we must take the square root of each side of the equation to get  by itself.

Doing this makes our problem look like $\displaystyle \sqrt{x^{2}}=\sqrt{49}$

Then we perform the square root to get the answer $\displaystyle x=\pm7$

Remember that $\displaystyle (-7)^{2}$ can also equal $\displaystyle 49$ so our answer will be both positive and negative.

The final answer looks like $\displaystyle x=\pm7$.

$\displaystyle 6e+8=14$

We need ot work to isolate the variable using inverse operations.

Subtract $\displaystyle \small 8$ from both sides.

$\displaystyle 6e+8-8=14-8$

$\displaystyle 6e=6$

Divide each side by $\displaystyle \small 6$.

$\displaystyle \frac{6e}{6}=\frac{6}{6}$

$\displaystyle e=1$

To solve $\displaystyle x+7=12*2$, start by simplifying the right side.

$\displaystyle x+7=12*2$

$\displaystyle x+7=24$

Now isolate $\displaystyle x$. This means we need to subtract $\displaystyle 7$ from both sides.

$\displaystyle x+7-7=24-7$

$\displaystyle x=24-7$

$\displaystyle x=17$

To solve for X, we must isolate X on one side of the equation.  In this case, we do this by subtracting 3X and adding 11 to both sides.

$\displaystyle (3X-3X)+(4+11)=(6X-3X)+(-11+11)$

$\displaystyle 15=3X$

We now have isolated X on one side of the equation, so we need only to reduce 3X to 1X.  We can do this by dividing both sides by 3:

$\displaystyle (15/3=3X/3)=(5=X)$

To solve for $\displaystyle x$, we need to isolate our variable. That means that we want ONLY the $\displaystyle x$ on the left side of the equation. But first, we need to combine our like terms on the right side.

$\displaystyle x-12=18+7$

$\displaystyle x-12=25$

Add $\displaystyle 12$ to both sides.

$\displaystyle x-12+12=25+12$

$\displaystyle x=25+12$

$\displaystyle x=37$

To perform a two-step algebra problem with addition and multiplication we must remove the numbers from  so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being added so we must subtract the number, $\displaystyle 44$, from each side of the equation $\displaystyle 9x+44-44=125-44$

Perform the math so our equation becomes $\displaystyle 9x=81$

Then we divide each side of the equation by the number that is in front of , $\displaystyle 9$, to get  by itself $\displaystyle \frac{9x}{9}=\frac{81}{9}$

Perform the math to find the answer $\displaystyle x=9$

To perform a two-step algebra problem with addition and division we must remove the numbers from  so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being subtracted so we must add the number, $\displaystyle 15$ , to each side of the equation 

$\displaystyle \frac{x}{2}-15+15=75+15$

Perform the math so our equation becomes

$\displaystyle \frac{x}{2}=90$

Then we multiply each side of the equation by the number that is under  to get  by itself 

$\displaystyle 2\cdot \left(\frac{x}{2}\right)=(90)\cdot 2$

Perform the math to find the answer $\displaystyle x=180$

The problem above is a two-step algebra problem with distribution.

To solve you must first distribute the $\displaystyle -8$ outside of the parentheses into both of the numbers inside by multiplying.

Remember when you distribute a negative that both of the numbers inside the parentheses are being multiplied by a negative number so they must flip signs.

Our problem now looks like $\displaystyle -8x+40=48$

Then we must get our variable, , by itself.

We must subtract the number, $\displaystyle 40$ , from each side of the equation $\displaystyle -8x+40-40=48-40$

Perform the math so our equation looks like $\displaystyle -8x=8$

Then we divide each side of the equation by the number that is in front of  to get  by itself $\displaystyle \frac{-8x}{-8}=\frac{8}{-8}$

Solve the math to find the answer $\displaystyle x=-1$

When there are variables and numbers on each side of the equation, to solve we must mathematically move the variables onto one side and the numbers onto the other.

To do this we put all of the variables on the right side of the equal sign by subtracting $\displaystyle x$ from the right and left side of the equation to have 

$\displaystyle x-x+89=5x-x+37$

When adding or subtracting variables you only add or subtract the numbers in front of the variables. If there is no number the number value is $\displaystyle 1$.

Perform the math 

$\displaystyle 89=4x+37$

Then to get all of the integers to the left side we will subtract $\displaystyle 37$ from the right and left side of the equation to have

 $\displaystyle 89-37=4x+37-37$

Perform the math 

$\displaystyle 52=4x$

At this point we must divide each side of the equation by the number that is in front of  to get  by itself $\displaystyle \frac{52}{4}=\frac{4x}{4}$

Perform the math to find the answer $\displaystyle \frac{52}{4}=x$

The answer is $\displaystyle x=13$.

To perform a two step algebra problem with addition and multiplication we must remove the numbers from  so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being added so we must subtract the number, $\displaystyle 83$, from each side of the equation

 $\displaystyle 5x+83-83=123-83$

Perform the math so our equation looks becomes

$\displaystyle 5x=40$

Then we divide each side of the equation by the number that is in front of , $\displaystyle 5$, to get  by itself 

$\displaystyle \frac{5x}{5}=\frac{40}{5}$

Perform the math to find the answer $\displaystyle x=8$